Question

You’re speeding at 85 km/hr when you notice that you’re only 10 m behind the car in front of you,
which is moving at the legal speed limit of 60 km/hr. You slam on your brakes, and your car negatively
accelerates at 4.2 m/s
2
. Assuming the other car continues at constant speed, will you collide? If so, at what
relative speed? If not, what will be the distance between the cars at their closest approach?

Answer 1

I am still confused of how close they actually get if they do not collide, could you explain how I could get this answer or show me?

Answer 2

Lets start afresh, when we use the third equation of motion\[v^2 =v^2_o +2as \]we are starting with initial relative velocity of 25 Km/hr (relative velocity is the rate at which the cars are moving with respect to each other) which is \[v_o= 6.944m/s\]For the collision to be avoided, this relative velocity must become zero before the clearance distance of 10 m is over\[s= 10m\]The velocity is decreasing because of the breaks, \[a= -4.2m/s^2\]Plug these values in the above equation and find 's'. This gives you the distance the cars would become stationary with respect to each other (relative velocity = 0) thus the closes that they ever are is (10- s) meters.